Inputs in the production function

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Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produce Y units of output according to the following production function: Y = 30K + 10L The firm wants to produce 600 units of output. 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical axis. 2. The shape of the isoquant tells us about the relationship between the two inputs in production. How substitutable are L and K in the production of Y ? In particular, how many units of L can be replaced by one unit of K without affecting the level of output? 3. Is this isoquant convex (bowed toward the origin)? 4. In class, we said that isoquants are convex under our “standard assumptions.” To see which standard assumption is violated in this case, hold K fixed at some level (for convenience, suppose K is fixed at zero). Graph Y as a function of L for L = 0, …, 5. 5. By looking at your graph, determine the marginal product of labor (MPL). That is, what is the change in Y (?Y ) when L increases by 1 unit (?L = 1)? 6. How does the marginal product of labor (MPL) change as L increases? How is this different from the “standard assumption” about the MPL we made in class? 7. Suppose the firm can choose whatever combination of capital (K) and labor (L) it wants to produce 600 units. Suppose the price of capital is $1,000 per machine per week. What combination of inputs (K and L) will the firm use if the weekly salary of each worker is $400?

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